Solution
= Solution
<Integration by parts>, whose boundary term vanishes for $\operatorname{Re}p>0$, gives
$$
\boxed{\overline t(p)=\int_0^\infty te^{-pt}\,dt=\frac1p\int_0^\infty e^{-pt}\,dt=\frac1{p^2}.}
$$
= Solution
<Integration by parts>, whose boundary term vanishes for $\operatorname{Re}p>0$, gives
$$
\boxed{\overline t(p)=\int_0^\infty te^{-pt}\,dt=\frac1p\int_0^\infty e^{-pt}\,dt=\frac1{p^2}.}
$$